As another answer mentions, AndroidViewClient using UiAutomator back-end cannot dump the content of any other than the main window, thus why the Input Method window is not accessible.
AndroidViewClient supports other back-ends, like ViewServer. You can take a look at the examples provided with AndroidViewClient source, particularly at dump-all-windows.py, which shows how to dump the content of other windows not just the main one.
Even though you can get most of the Views in the keyboard, the actual keys are handled internally by com.android.inputmethod.keyboard.internal.PreviewPlacerView
and thus you won't be able to interact with them individually.
Remember that you can always touch the keys using their coordinates like in
if device.isKeyboardShown():
device.touch(400, 950)
that would touch the G on a 768x1280 emulator. But this is device dependent.